This is the second in a series of postings about correlation modelling. In the first posting we discussed the idea of correlation as representing a proxy model of dependency between random variables. In this posting, we discuss the idea the often overlooked concept that relationships of correlation do not necessarily imply any directionality.
In modelling time series of financial asset prices, it is common practice to correlate the changes (returns) in prices (within each period). One way to see that the variables will not necessarily trend in the same direction is by simple reference to the formula for correlation (see for example Excel’s Help and search for the CORREL function). The formula is based on the differences of each point from the average. If for example one variable has a positive average change and the other a negative average change, then they will drift in different directions, even if the changes are positively correlated. Correlation refers to the idea that each variable moves relative to its own average in a common way.
The screenshot shows an example of two times series with this property; one has a positive average drift and the other a negative average drift, and the series have a positive correlation coefficient of 34%.
Capturing the directionality between variables is something that requires a different modelling approach, such as establishing the long-run equilibrium of the spread, ratio, or differences between the prices and modelling these. This is the topic of co-integrated time series, which are becoming more and more important in financial econometrics, and will be the subject of a future posting.
Dr. Michael Rees
Director of Training and Consulting